Let be an acute angle such that .

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Let θ\theta be an acute angle such that cos⁡θ−sin⁡θ=0\cos \theta - \sin \theta = 0. (a) Prove that θ=45∘\theta = 45^\circ. (b) Using this value of θ\theta, find (a) sin⁡θ+cos⁡θ\sin \theta + \cos \theta and (b) tan⁡θ\tan \theta. (c) Show that (sin⁡θ+cos⁡θ)2=1+sin⁡2θ(\sin \theta + \cos \theta)^2 = 1 + \sin 2\theta for this value of θ\theta.

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